Infinity

#1

I imagine this topic has been touched, and retouched upon, but I figured I'd give it a stab. I was posting on another forum that will remain nameless, and my post was something to the effect of. "If you rolled 10 dice an infinite amount of times, eventually they would come up all 6s, but this wouldnt happen just once, but an infinite amount of times", To which there was a reply something like "It is possible that you could roll them an infinite amount of times and never come up all 6s". I found this quite a ridiculous idea, being that within infinity all possibilities are represented an infinite amount of times. Any thoughts?

#2

Cantor, who is the father of infinite sets, agrees with the reply you recieved. It could be completely possible to never roll all 6's. In fact, without considering other factors, it is more probable on any given roll that you will not have ANY sixes.

Your static chances of rolling the same result on ten six-sided dice is 0.00005954%. This increases if you disallow results, but that makes it a finite set, so it can not apply. Thus, you have established it as an open infinite set, have made a possiblity to have recurring results in an infinite loop. This means you have a 1/1,679,616 of getting a common result on all dice rolls. Thus, you have a 1/10077696 chance of getting all sixes on all ten dice.

Thus, you have a 1 in more than 10 Million 77 thousand chance of having it happen ONCE. (this is just based on raw random number probablity,.. there are other factors which would definitely affect this, such as an individual frequency of numbers for the person rolling, or force applied and angle of the dice.) This becomes a 1/335147870057728 chance of it happening ten times in a row. The only way you guarantee it will happen is in you may it an absolute null infinite set, where you ensure the set has all probabilities represented at least (greater than negative-zero times).

#3

Without trying to sound too simple about the whole thing, I imagine a dice game going...With 10 dice, rolling a 60...I see that has an extreme, but possile long shot...If you roll them fuckers 1,000,000 times, I'd like to think that at least once of those times, you'd hit 60...But that shit is CRAZY unlikely, but not impossible...You could use the force like Qui Gonn to move the dice tho, and that would help... /:D" style="vertical-align:middle" emoid=":D" border="0" alt=":D" />

Unlikely, but not impossible...I see what you're saying, an infinite amount of rolls would mean an infinite amount of 60's...But given our current number set...

I couldn't be arsed to do the math, LoL, but the largest known prime number (a number divisible by one and itself) is 2[sup:84da54217e]30402457[/sup:84da54217e]-1 which has 9152052 digits...If you could hook up some division, I'm curious to know the probability of rolling a 60 w/that prime in mind...

#4

Hmm, I'm kinda lost so far...

When this gets resolved...

Actual infinite does not exist, right? Only potential infinite does, or so I thought...but I always wondered, could/how could an actual infinite exist?

#5

QUOTE(raum)Cantor, who is the father of infinite sets, agrees with the reply you recieved. It could be completely possible to never roll all 6's. In fact, without considering other factors, it is more probable on any given roll that you will not have ANY sixes.

Your static chances of rolling the same result on ten six-sided dice is 0.00005954%. This increases if you disallow results, but that makes it a finite set, so it can not apply. Thus, you have established it as an open infinite set, have made a possiblity to have recurring results in an infinite loop. This means you have a 1/1,679,616 of getting a common result on all dice rolls. Thus, you have a 1/10077696 chance of getting all sixes on all ten dice.

Thus, you have a 1 in more than 10 Million 77 thousand chance of having it happen ONCE. (this is just based on raw random number probablity,.. there are other factors which would definitely affect this, such as an individual frequency of numbers for the person rolling, or force applied and angle of the dice.) This becomes a 1/335147870057728 chance of it happening ten times in a row. The only way you guarantee it will happen is in you may it an absolute null infinite set, where you ensure the set has all probabilities represented at least (greater than negative-zero times).

I dont quite understand what you guys are getting at. The numbers really dont mean anything. I could have used any far off possibility. I dont think you can look at infinity as something quantifiable. It will happen the same amount of times regardless, because you are rolling the dice an infinite amount of times. The only way that statement could be true (the reply to me) is if you replaced never ever with some finite quantity, then it would be true, approaching infinity, but never reaching it. The discussion we were having was order and chaos. And I said within an infinite amount of chaos exists and infinite amount of order, and if you were to exist within the order, you would assume that everything was ordered.

#6

I think the point raum was trying to make (and I'm sure he'll correct me if I overstep my bounds) is that for there to be one roll of all 6's (or whatever combination you so desire) the odds are one in over 100 million. That's for each and every individual roll, whether you roll them once or an infinitie number of times. Therefore the possibility exists that even with an infinite number of rolls, you will never roll all 6's. The odds of this occuring will not change with successive rolls, each roll has the same odds of occuring, so the possibility is there.

#7

QUOTE(deepdiver32073)I think the point raum was trying to make (and I'm sure he'll correct me if I overstep my bounds) is that for there to be one roll of all 6's (or whatever combination you so desire) the odds are one in over 100 million. That's for each and every individual roll, whether you roll them once or an infinitie number of times. Therefore the possibility exists that even with an infinite number of rolls, you will never roll all 6's. The odds of this occuring will not change with successive rolls, each roll has the same odds of occuring, so the possibility is there..

That would work for every finite value, but not if you made it an infinite amount of rolls, the ratios would suddenly become completely useless, and every possible roll would be expressed an infinite amount of times. I know it seems like a goofy concept but with infinity you can add to it and it wont get any bigger, or subtract and it wont get smaller, or divide or multiply etc etc. So what makes you think a ratio would somehow be able to limit an infinite series? I dont think you are quite getting the scope of what i'm saying. Thats like saying whats 10^65000000000000000000000 * 0? And having to do calculations to figure out how big the number is before you know the obvious answer.

#8

exactly, the key is infinite sets.

for example, Your static chances of rolling 10 non-consecutive 60's is ONE in Three Hundred Thirty-Five TRILLION, One hundred Fourty-Seven BILLION, Eight Hundred Seventy MILLION Fifty-Seven THOUSAND, Seven Hundred Twenty-Eight.

keep in mind this is a static chance... it has a HUGE number of factors that need to be considered before it represents a REAL probablitity. For example, what if a given person throws sixes with an 36% consistency if they use their left hand, a 19% consistency if they use green dice, and a 56% consistency if they kiss the four-pip before tossing the dice.

By defining the infinite set to an infinite repetition of specifically left handed rolls with green dice that have been kissed on the four-pip, you create a modifier that statistically increases your chances approximately as represented below.

1/335,147,870,057,728

to

26,249,049,973/335,147,870,057,728

Basically you increase you chances by 26 BILLION times.

This means instead of having a 1 in 335 Billion chance (less than .000000000000002%) of getting a sixty ten consecutive times, you have actually given yourself a solid 7.8% chance by using green dice left-handed, with a kiss on the four-pip. But, there, by this logic, would be many other factors that would work for or against you. The more you isolate and control the conditions of the dice roll, the more likely you can control the outcome.

The confusion comes from the lack of specifying WHAT KIND of INFINITY the set is employing. And infinite set can be infinite in a number of ways. An absolute (or potentially) infinite set would have every possible result occur at least >-0 (more than negative zero) times. A real (or Actual) Inifinite Set would have every result occur at least one time. A Null infinite set would have each result occur at least zero times. There are others but you get the point. It could be possible to have an infinite set resulting in only 10's and 20's and 50's, but never EVER resulting in a 60.

But if the set is defined as infinite (∞) and you EVER get a different result than 60, x <= you have (∞)-1. Thus this would be a Potenially infinite set, which is the only infinity you could absolutely approximate with ten six-sided dice. The reason is simple, for there to be a recognition of 60, there must be at least one other representation in the cardinality of the infinite set of results that represents in some way n<>x=(∞)-1. Philosophically, this means for there to be any recognition of "60", there must be a recognition of "not 60". otherwise it is a Prime infinite set, and there is no reason to roll the dice, for there is only one possible outcome, and it in infinite. Your head would asplode trying to process the first dice roll, with no point of outside reference.

vertical,
raum

#9

Maybe I have been out of school too long, but from what I recall from statistics an infinite set has an infinite number of possibilites. Therefore, it only seems logical to me that if you roll an infinite number of times, there has to be possibility of rolling no 60's just as is the possibility of rolling several 60's...

Where's Tron at when u need him?...Bet u he could hit those 60's a couple of times... /laugh.gif" style="vertical-align:middle" emoid=":lol:" border="0" alt="laugh.gif" />

#10

ark, yup,.. exactly. there are No less than 335 TRILLION MORE possibilities of rolling NO Sixties that rolling TEN, much less an infinite number of 60's.